Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
279 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 279 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10589329 | C2 | semidirect |
| 3. C3×#4463 | C2 | semidirect |
| 5. #10589105 | C2 | semidirect |
| 27. #4463 | D3 | semidirect |
| 198. C32 | #2165 | semidirect |
| 229. C3 | #69298 | semidirect |
| 230. C3 | #69864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×ΓL(1,𝔽25) | 2 |
| #10589329 | 2 |
| C3×#4463 | 2 |
| #10589109 | 2 |
| #10589105 | 2 |
| #69864 | 3 |
| #69298 | 3 |